Frontiers: Air Bubble in Water

This example corresponds to section 3.4 in our publication. In this example we study the acoustic radiation force (ARF) on an air bubble suspended in water.

As always we start off by importing the necessary Python modules. For our example we are going to need the osaft library, and the third party packages NumPy and Matplotlib.

import numpy as np
from matplotlib import pyplot as plt

import osaft

The next step is to define the properties for our example, these include the material properties, the properties of the acoustic field and the radius. We always assume SI-units.

The wave type is set using the osaft.WaveType enum. Currently, there are two options: osaft.WaveType.STANDING and osaft.WaveType.TRAVELLING for a plane standing wave and a plane travelling wave, respectively.

# --------
# Geometry
# --------
# Radius
R_0 = 5e-6  # [m]

# -----------------
# Properties of Air
# -----------------
# Speed of sound
c_air = 343  # [m/s]
# Density
rho_air = 1.225  # [kg/m^3]

# -------------------
# Properties of Water
# -------------------
# Speed of sound
c_w = 1_498  # [m/s]
# Density
rho_w = 997  # [kg/m^3]

# --------------------------------
# Properties of the Acoustic Field
# --------------------------------
# Frequency
f = 5e5  # [Hz]
# Pressure
p_0 = 1e5  # [Pa]
# Wave type
wave_type = osaft.WaveType.STANDING
# Position of the particle in the field
position = np.pi / 4  # [rad]

Once all properties are defined we can initialize the solution instances. osaft.yosioka1995.ARF() is the class for computing the ARF using the model by Yosioka and Kawasima (1955).

Here we give the instances different names 'General' and 'Bubble' by setting the name attribute. This makes sure we can later distinguish them when the solutions are plotted.

# General
yosioka = osaft.yosioka1955.ARF(
    f=f,
    R_0=R_0,
    rho_s=rho_air,
    c_s=c_air,
    rho_f=rho_w,
    c_f=c_w,
    p_0=p_0,
    wave_type=wave_type,
    position=position,
)
yosioka.name = "General"

# Small bubble approximation
yosioka_bubble = yosioka.copy()
yosioka_bubble.small_particle = True
yosioka_bubble.bubble_solution = True
yosioka_bubble.name = "Bubble"

With the class osaft.yosioka1955.ARF() it is also possible to plot the acoustic fields. Here, we first set the frequency to 6.5e5 Hz. Then we initialize a osaft.FluidScatteringPlot() instance which will plot the acoustic field in the fluid. The class takes the model as an argument and the radius range r_max that is plotted. For more option see the documentation.

The method plot() will then generate the plot. As always with Matplotlib, we need to call plt.show() to display it.

# Setting frequency close to resonance
yosioka.f = 6.5e5

# Initializing plotting class
scattering_plot = osaft.FluidScatteringPlot(yosioka, r_max=3 * yosioka.R_0)

# Plot scattering field
fig, ax = scattering_plot.plot_velocity()

plt.show()

To animate the acoustic field we can call the method animate(). Setting incident = False means that we are only animating the scattered field but not the incident field.

anim = scattering_plot.animate_velocity(
    frames=20,
    interval=100,
    incident=False,
)

plt.show()

Once Loop Reflect

Finally, we want to compare the general solution for the ARF with the approximate solution for a bubble. To plot the ARF we need to initialize osaft.ARFPlot() instance. With the method add_solutions() we can add our models to the plotter. With set_abscissa() we define the variable that we want to plot the ARF against. Here we select the frequency f. Finally, osaft.ARFPlot.plot_solutions() will generate the plot. Again, we call plt.show() to display it.

# sphinx_gallery_thumbnail_number = -1
# Initializing plotting class
arf_plot = osaft.ARFPlot()

# Add solutions to be plotted
arf_plot.add_solutions(yosioka, yosioka_bubble)

# Define independent plotting variable (in this case the frequency)
arf_plot.set_abscissa(x_values=np.linspace(1e5, 1e6, 300), attr_name="f")

# Plot the ARF
fig, ax = arf_plot.plot_solutions()

# Setting the axis labels
ax.set_xlabel(r"$f$ $\mathrm{[Hz]}$")

plt.show()

Note

It is only possible to plot the ARF against properties that wrap an underlying PassiveVariable, i.e. an input parameter of the model. You can get a list of all input variables using the method input_variables().

print(f"{yosioka.input_variables() = }")

yosioka.input_variables() = ['small_particle', 'bubble_solution', 'position', 'p_0', 'wave_type', 'rho_s', 'c_s', 'rho_f', 'c_f', 'R_0', 'f', 'N_max']

Estimated memory usage: 9 MB